New sub project - Wieferich and Wall-Sun-Sun Prime Search

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Alez
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#1 New sub project - Wieferich and Wall-Sun-Sun Prime Search

Post by Alez »

From prime grid forum announcment

Welcome to the Wieferich and Wall-Sun-Sun Prime Search

A Wall–Sun–Sun (or Fibonacci–Wieferich) prime is a prime p > 5 in which p^2 divides the Fibonacci number Image , where the Legendre symbol Image is defined as Image

They are named after Donald Dines Wall and twin brothers Zhi-Hong Sun and Zhi-Wei Sun. Drawing on Wall's work, in 1992 the brothers proved that if the first case of Fermat's last theorem was false for a certain prime p, then that p would have to be a Wall–Sun–Sun prime.

Although it has been conjectured that infinitely many exist, there are no known Wall–Sun–Sun primes. As of December 2011, if any exist, they must be > 9.7e14. The PRPNet search began here, and the BOINC search will as well for double-checking purposes.

The lack of success has lead to an interest in "Near" Wall-Sun_Sun primes. They are defined as special instances (with small |A|) of F_(p-(p/5)) = Ap (mod p^2).

A prime p is a Wieferich prime if p^2 divides 2^(p-1) - 1. They are named after Arthur Wieferich who in 1909 proved that if the first case of Fermat’s last theorem is false for the exponent p, then p satisfies the criteria a^(p-1) = 1 (mod p^2) for a=2.

Notice the similarity in the expression p^2 divides 2^(p-1) - 1 to the special case of Fermat's little theorem p divides 2^(p-1) - 1.

Despite a number of extensive searches, the only known Wieferich primes to date are 1093 and 3511. The rarity of these primes has lead to an interest in "Near" Wieferich primes. They are defined as special instances (with small |A|) of 2^((p−1)/2) ≡ ±1 + Ap (mod p^2).
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Alez
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#2 Re: New sub project - Wieferich and Wall-Sun-Sun Prime Search

Post by Alez »

Classes as new sub project on WUProp to. Rare chance these days for a new star.
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#3 Re: New sub project - Wieferich and Wall-Sun-Sun Prime Search

Post by Miklos M »

I am running WW this morning, the credit is not bad, 4000 points for 5+ minutes on 2080 ti.
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Alez
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#4 Re: New sub project - Wieferich and Wall-Sun-Sun Prime Search

Post by Alez »

@70 mins on a 980. Same fixed credit.
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#5 Re: New sub project - Wieferich and Wall-Sun-Sun Prime Search

Post by Dirk Broer »

@25 mins. run time on a 1650. CPU time 20 sec. average (15.25-16.75)
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#6 Re: New sub project - Wieferich and Wall-Sun-Sun Prime Search

Post by Granowski »

greetings ... I have 6000 wu sent for Wieferich ... no find unfortunetly ...

regards, Gregg Roman Granowski ...

Let's solve Sierpiński Problem TOGETHER ...
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#7 Re: New sub project - Wieferich and Wall-Sun-Sun Prime Search

Post by Miklos M »

Alez wrote: Mon Nov 30, 2020 1:12 pm Classes as new sub project on WUProp to. Rare chance these days for a new star.
I think the badges are trailing the wu's. But, we shall see very soon.
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#8 Re: New sub project - Wieferich and Wall-Sun-Sun Prime Search

Post by Gibson Praise »

Credit is supposed to be the roughly the same as running the AP project . .
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#9 Re: New sub project - Wieferich and Wall-Sun-Sun Prime Search

Post by Miklos M »

Gibson Praise wrote: Tue Dec 01, 2020 3:52 pm Credit is supposed to be the roughly the same as running the AP project . .
Sounds good, ty for the info.
Is Moo w :? rapper giving badges( I started hunting them, lol)
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